# Homework Help: Math: Calculus

## Recent Homework Questions About Calculus

**basic calculus**

A page is to contain 54 square centimeters of printed material. If the margins are 1 cm at the top and bottom and 0.5 cm at the sides, find the most economical width of the page (in cm).

*Saturday, February 11, 2017 by james*

**Calculus**

Show that there are at least two values of x in the interval (−π,π) such that x=1+sin(x)

*Saturday, February 11, 2017 by Larin*

**Calculus 2**

I cannot figure this out for the life of me. Maybe I am overthinking it. Money is transferred into an account at the rate of R(t)=5000t(e^-0.6t) If the account pays 2% interest compounded continuously, how much will accumulate in the account over a 9-year period?

*Friday, February 10, 2017 by Alexis*

**Calculus prince@18**

let the function h(x)= (integrand symbol from 2 to x^2)arctan (t) dt. Find h'(x). This question confused me because i know the derivative of an integral is the original function. I just need help with finding the derivative of that integral. I don't know how to post integral ...

*Thursday, February 9, 2017 by Prince@18*

**Calculus**

Suppose that a car dealer offers to sell you a car for $16500 or for payments of $275 per month for six years. To figure out what monthly interest (x) you’re actually being charged, you’d have to solve the equation:f(x)=60x(1+x)^72-(1+x)^72+1=0

*Thursday, February 9, 2017 by Emily*

**calculus**

a toy balloon is in the shape of a sphere. it is being inflated at the rate of 20 in^3 / min. at the moment that the sphere has volume 64 cubic inches. what is the rate of change of the radius ?

*Thursday, February 9, 2017 by ivy*

**Calculus review**

let the function h(x)= (integrand symbol from 2 to x^2)arctan (t) dt. Find h'(x). This question confused me because i know the derivative of an integral is the original function. I just need help with finding the derivative of that integral. I don't know how to post integral ...

*Thursday, February 9, 2017 by Prince@18*

**calculus**

Find the points on the graph y = -x^3 + 6x^2 at which the tangent line is horizontal. I found -x^2 + 4 = 0 are the points [4,32]

*Wednesday, February 8, 2017 by heather*

**Calculus unit review**

I wanted to ask this 1 questions because i didn't even know where to start. For a continuous function f(x), f(1) = 11, and Integral symbol from 1 to 5 f'(x)dx=9. Find f(5).

*Wednesday, February 8, 2017 by Prince@18*

**Continuity Calculus Help**

Find the value of constants c and d that make the function below continuous at x = 4. f(x) = x2 − 3x x < 4 c x = 4 d + x x > 4 c = d = 8 I got d=8, but finding c is giving me trouble.

*Wednesday, February 8, 2017 by John*

**Continuity Calculus Help**

9.0/1 points | Previous Answers SSTCalc6 2.3.046.My Notes Question Part Points Submissions Used Let f(x) = 4x2 if x > 2 4x + 3 if x ≤ 2. Show that f is continuous from the left at x = 2, but not from the right. lim f(x) = n→2− f(2) = lim f(x) = n→2+

*Wednesday, February 8, 2017 by John*

**Continuity Calculus Help**

The given function is defined for all x > 0 except at x = 8. Find the value that should be assigned to f(8), if any, to guarantee that f will be continuous at 8. (If an answer does not exist, enter DNE.) f(x)= Sqrt( x^2-64/x-8)

*Wednesday, February 8, 2017 by Carli Minacapel*

**Calculus-derivatives**

At what points on the graph of f(x)=6x^2+4x-9 is the slope of the tangent line -2?

*Wednesday, February 8, 2017 by Angel*

**physics/calculus**

A stone is thrown straight up from the edge of a roof, 600 feet above the ground, at a speed of 12 feet per second. A. Remembering that the acceleration due to gravity is -32 feet per second squared, how high is the stone 6 seconds later? B. At what time does the stone hit the...

*Tuesday, February 7, 2017 by kloe*

**Calculus**

My question is with a multi-part homework assignment that we got in class. The information given is : A factory manufactures widgets. The rate of production of widgets after t weeks is widgets/ week. The equation for this is dx/dt=30(1-(20/((t+20)^2))). The actual questions ...

*Tuesday, February 7, 2017 by Noah*

**Calculus :**

The rate at which ice in a skating pond is melting is given by dV/ft = -4t - 2 Where V is volume of the ice in cubic inches and t is time in days after March 1st. Skaters can use the pond as long as the volume is greater than 3 cubic ft. If the ice is 5cubic ft in march 1st, ...

*Monday, February 6, 2017 by Char*

**Calculus**

Given: A rock is thrown upward from the surface of a planet at 24m/s. It reaches a maximum height of 180 meters. Question: How fast is the rock falling when it lands on the planet? I am honestly dumbfounded by this problem. I feel that I don't have enough information, I don't ...

*Monday, February 6, 2017 by Charlene*

**Pre-Calculus**

determine the projection of u = 1.6 vector i + 3.3 vector j in the vector v = -2.1 vector i - 0.5 vector j direction

*Sunday, February 5, 2017 by Trish*

**Pre-Calculus**

a jet, in calm air conditions, travel with velocity vector (389, 389). the wind velocity (in mph) at the plane's cruising altitude is given by (0, 50). how fast is the plane's true speed

*Sunday, February 5, 2017 by Trish*

**Calculus**

Find the magnitude and direction angle of p=42i+35j

*Saturday, February 4, 2017 by Elise*

**Calculus**

Find the magnitude and direction angle of p=42i+35j

*Saturday, February 4, 2017 by Rachel*

**Calculus**

For which values of x does the curve Y= (3x^3-3x^2+1) / (2x^2-1) , have a horizontal tangent? Show steps or explain, i dont get it

*Friday, February 3, 2017 by Carmen*

**Calculus**

Comute f(x) of a) f(x) = sinxcosx / sinx + cosx b) f(x) = (1-x^2) / (1+x+x^2) c) f(x) = x^7 secx

*Friday, February 3, 2017 by Jessi*

**Calculus**

Knowing that F(-2) = -7, F'(-2)= 12, g(-2)= -3 and g'(-2)= -9, Compute: a) h'(-2) if h(x)= f(x)g(x) b) h'(-2) if h(x) = f(x) / g(x) c) h'(-2) if h(x) = g(x) / 1+(f(x))^2 Show all steps

*Friday, February 3, 2017 by Mikey*

**Calculus**

Let F(x) = (x+1) / (x^2-16). Use the definition of the derivative to compute f'(x) and give its domain. Show all steps.

*Friday, February 3, 2017 by jaime*

**Calculus**

A population of 1200 badgers grow by 6% every 8 years. How long does it take the population of badgers to grow 2000?

*Friday, February 3, 2017 by Gary*

**calculus**

Find the volume of a solid whose base is bounded by the parabola x=y^2 and the line x=9, having square cross-sections when sliced perpendicular to the x-axis.

*Friday, February 3, 2017 by Ethan*

**Calculus**

Write an expanded polynomial equation based on the following information. A cubic function with a zero x=3 (with multiplicity 2), a zero at x=2, and a constant term of 18.

*Thursday, February 2, 2017 by Jay*

**calculus**

limx--->3- 5/x-3 I think it is -inf but I don't know how to prove it

*Thursday, February 2, 2017 by heather*

**calculus**

A student throws a ball upward from a height of 48ft, initially at 32ft per second. What is the maximum height of the ball?

*Thursday, February 2, 2017 by Haze*

**calculus**

if limit x--->0(4-g(x)/x)=1

*Thursday, February 2, 2017 by heather*

**calculus**

limx--->0 3sin 3x/4x would it be 9/4

*Wednesday, February 1, 2017 by sarah*

**Help! Calculus**

I am so confused on how to solve this problem. I have it set up with y's on one side and x's on the other but I don't know what to do from there. Question: Solve the differential equation. The initial condition is y(0) = 1. ((x^2+1)^(1/2))(dy/dx) - (x/(2y)) = 0 y > 0 My ...

*Wednesday, February 1, 2017 by Lucy*

**calculus**

limx-->3 sin 3x/4x

*Wednesday, February 1, 2017 by sarah*

**calculus**

find the average rate of change of the function f(x)=x^3+1 over the interval [-1,1]

*Wednesday, February 1, 2017 by Anonymous*

**calculus**

Argus Company makes three products: A, B, and C. Each unit of A costs $4, each unit of B costs $2, and each unit of C costs $1 to produce. Argus must produce at least 20 As, 30 Bs, and 40 Cs, and cannot produce fewer than 200 total units of As, Bs, ...

*Wednesday, February 1, 2017 by namasya*

**calculus**

if limx-->0(4-g(x)/x=1find limx--->0g(x)

*Wednesday, February 1, 2017 by Anonymous*

**calculus**

find the limit x-->inf (x^2+x)^1/2-(x^2-x)^1/2 so I know I multiply by the conjugate 2x/(x^2+x)^1/2+(x^2-x)^1/2 then I don't know where to finish problem

*Wednesday, February 1, 2017 by kim*

**Calculus**

True or False,... Im confused If the continuous function f(x) has a domain (-∞, +∞), then either lim --> ∞ exists, or limit X--> ∞ is +-∞

*Tuesday, January 31, 2017 by LJ*

**basic calculus**

x^3+x^2y+2y^2=0

*Tuesday, January 31, 2017 by elijeh*

**basic calculus**

x^3+x^2y+2y^2

*Tuesday, January 31, 2017 by elijeh*

**basic calculus**

find a appropriate formula for the area of a narrow circular ring....wedding band made of circular wire

*Tuesday, January 31, 2017 by elijeh*

**basic calculus**

find a appropriate formula for the area of a narrow circular ring

*Tuesday, January 31, 2017 by elijeh*

**Calculus AB**

What's the lim(x-->-infinity) sqrt(x^4-1)/(x^3-1)? I've tried solving for it but I got -1/0, which would make it undefined. Is that correct?

*Tuesday, January 31, 2017 by Annie*

**Calculus AB**

So the problem is "For x>0, d(lnx)/dx = 1/x and lne=1. A) find the tangent line approximation for ln 3 B) calculate the %error in approximation in part A. My teacher said the answer for part A is that 1/e, and I'm pretty confused. So far I the given info into point slope ...

*Monday, January 30, 2017 by Annie*

**Pre-Calculus**

How to solve sin(x/2) = 1 - cos x? I know you would use the half angle identity sin(x/2) = +-(√1 - cos x/2), just don't know what to do from there.

*Monday, January 30, 2017 by Karen*

**Pre-Calculus**

How to solve sin(x/2) = 1 - cos x? I know you would use the half angle identity sin(x/2) = +-(√1 - cos x/2), just don't know what to do from there.

*Monday, January 30, 2017 by Karen*

**Calculus II**

Sketch the region R defined by 1 ≤ x ≤ 2 and 0 ≤ y ≤ 1/x3. a) Find (exactly) the number a such that the line x = a divides R into two parts of equal area b) Then find (to 3 places) the number b such that the line y = b divides R into two parts of equal area

*Monday, January 30, 2017 by Angel Santos*

**applied calculus**

From a height of 25 meters a ball is thrown vertically upwards at a velocity of 5 meters per second. a.What time in seconds will the ball reach its maximum height? b.What is its maximum height? c.When will the ball strike the ground? d.What will be the ballâ€™s velocity ...

*Sunday, January 29, 2017 by Laura*

**Calculus**

I am having trouble with this question and I am unsure how to solve it... True or False (with justification) The function sin(x) if x ≤ 0 f(x) = 1+cos(x) if x>0 has a jump discontinuity at x = 0.

*Sunday, January 29, 2017 by Emily*

**calculus**

I have a definition lim theta approaching 0 sin theta/theta = 1 so show if the limit x approaching 0 sin2x/5=2/5

*Sunday, January 29, 2017 by sarah*

**calculus**

define f(x)={x+a if x>2 {-1 if x=2 {ax+b if x<2. How to determine the values of a and b for which f(x) is continuous in the set of real numbers.

*Sunday, January 29, 2017 by Angel*

**calculus**

Define h(x)={x^2 if x>=-1 {ax+b if x<-1 If f(-2)=-1, how do i determine the values of a and b for which h(x) is continuous in the set of real numbers

*Sunday, January 29, 2017 by Qin*

**calculus**

Let g(x)={x^2-x-2 if x is not equal to 1 {0 if x=1

*Sunday, January 29, 2017 by Liv*

**Calculus can you please show me the step by step s**

The intensity of light varies inversely as the square of the distance from its source. If two searchlights are 600 meters apart and one light is 8 times as strong as the other, where should a man cross the line between them in order to be illuminated as little as possible

*Saturday, January 28, 2017 by John*

**Calculus**

The intensity of light varies inversely as the square of the distance from its source. If two searchlights are 600 meters apart and one light is 8 times as strong as the other, where should a man cross the line between them in order to be illuminated as little as possible

*Saturday, January 28, 2017 by John*

**basic calculus**

The area of the surface of a sphere of radius r is 4πr^2. If the estimate radius of a spherical balloon is 200 meter and this estimate is too small by 1/2 meter. Find the approximate surface area in sq. m.

*Friday, January 27, 2017 by yumie*

**calculus**

A stone thrown up from the top of a building with a velocity of 48 meter per second reaches the ground with a velocity of -50 m/s. Find the height of the building. Using the derivative of approximation.

*Friday, January 27, 2017 by airrah mae*

**Calculus**

Find the vertical translation of y=|x| that "supports" the parabola y = x^2. Hint: You should find 'c' so that y = |x|+c just touches y = x^2. You may as well consider only the right-hand side of the picture first. (Why?)

*Thursday, January 26, 2017 by Anonymous*

**Applied Calculus**

From a height of 25 meters a ball is thrown vertically upwards at a velocity of 5 meters per second. a. What time in seconds will the ball reach its maximum height? b. What is its maximum height? c. When will the ball strike the ground? d. What will be the ball’s velocity ...

*Thursday, January 26, 2017 by jay*

**Calculus**

Let A denote the portion of the curve y = sqrt(x) that is between the lines x = 1 and x = 4. 1) Set up, don't evaluate, 2 integrals, one in the variable x and one in the variable y, for the length of A. My Work: for x: âˆ«[4,1] sqrt(1+(dy/dx)^2) dy/dx = 1/2sqrt(x) (dy/dx)^2...

*Wednesday, January 25, 2017 by Daisy*

**calculus**

find the limit without using L'Hopital's Rule Lim(X->-4) (16-x^2 / x+4)

*Wednesday, January 25, 2017 by jaime*

**Calculus**

Knowing that Pi/2 < x < Pi and that 0<y< Pi/2 that sinx = 1/5 and that cos y = 1/8, find sin (x+y), sin (x-y), cos (x+y) and cos (x-y). Explain.

*Wednesday, January 25, 2017 by MArc*

**calculus**

Use implicit differentiation to find an equation of the tangent line to the curve 3xy^3+4xy=63 at the point (9,1)(9,1).

*Wednesday, January 25, 2017 by gloria*

**calculus**

A spherical balloon is inflated so that its volume is increasing at the rate of 3.2 ft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.1 feet?

*Wednesday, January 25, 2017 by gloria*

**Calculus**

Find two non-intersecting intervals where f(x) +12x^4 + 50x^3 + 80x^2-100 has at least one root. Justify your answer.

*Tuesday, January 24, 2017 by MArc*

**Calculus**

Compute F'(-4) where F(x) = x^3 + X^2 (using the definition of the derivative)

*Tuesday, January 24, 2017 by Justine*

**Calculus**

Find all the values of (x) in the interval [0, 2Pi], such that sec^2 (x) = 4

*Tuesday, January 24, 2017 by Severin*

**Calculus**

A manufacturer buys $280,000 worth of machinery that depreciates linearly so that its trade-in value after 10 years will be $30,000. Express the value of the machinery (V) as a function of its age (t).

*Tuesday, January 24, 2017 by jaaaay*

**Calculus**

y = 2 cos(5πx) .... whats the period?

*Tuesday, January 24, 2017 by Anonymous*

**Calculus**

Find the equation in standard form for the line that satisfies the given requirements. horizontal line through (−8, −9)

*Tuesday, January 24, 2017 by Anonymous*

**Calculus**

Piecewise function x if −2≤x≤0; x^2 if −2<x<0; 8-x. If if −2≤x≤3; (d) Write down an analytic formula for f^{-1}, and state its domain and range.

*Tuesday, January 24, 2017 by Po*

**Calculus**

Solve the quadratic equation by factoring. (Enter your answers as a comma-separated list.) 5x2 − 23x = −12

*Tuesday, January 24, 2017 by jay*

**Calculus**

Can you please check to see if these answers are correct? I have provided my work as well! That you! This is much appreciated!! 1. What is the volume of the solid that is generated by revolving the region bounded by the curves x = 3y^2-2 and x = y^2 and y = 0 about the x axis...

*Monday, January 23, 2017 by Daisy*

**Pre-Calculus**

The base of the fish tank below has a length of 40 inches, a width of 20 inches, and height of 1.5 feet. The tank starts off with a water depth of 7 inches. You then add water to the tank at a constant rate such that the water level increases 1 inch every 2 minutes. Wirte a ...

*Monday, January 23, 2017 by Tod*

**Calculus**

Find inverse equation of y= 3e^(x-1)^5 Answer I got is (ln(x/3))^(1/5) +5 =y But I think it's wrong because the domain and range is really different from the original equation

*Sunday, January 22, 2017 by Po*

**calculus**

A 17- foot ladder is leaning against a wall, and begins to slide. The top of the ladder is falling at a rate of 2 feet per second at the instant that the bottom of the ladder is 8 feet from the wall. What is the rate of change of the distance between the bottom of the ladder ...

*Sunday, January 22, 2017 by angie*

**calculus**

The mechanics at lincoln automotive are reboring a 6-in. deep cylinder to fit a new piston. The machine they are using increases the cylinder's radius 0.02 inches each second. How rapidly is the cylinder volume increasing when the bore (diameter) is 3.8 in.?

*Sunday, January 22, 2017 by judy*

**calculus**

Melissa wants to make a rectangular box with a square base and cover its top and bottom faces with velvet, which will cost her $3 per square inch, and the sides with silk, which will cost her $5 per square inch. The box should have a volume of 1600 cubic inches. Find the ...

*Sunday, January 22, 2017 by judy*

**Calculus**

Does F(x)=9-x^2 satisfy the hypothesis of the mean value theorem on the interval [0,3]? if it does, then find the exact values of all Ce(0,3) that satisfy the conclusion of the Mean Value Theorem.

*Sunday, January 22, 2017 by Angie*

**Calculus**

Consider the function f(x) = -3x+2. Notice the limit of f(x) as x approaches 1 is -1. Find a value for delta such that is the distance x is from 1 is less than delta, then the distance from f(x) to -1 is less than 0.05

*Sunday, January 22, 2017 by Jeff*

**maths calculus also**

what is the area enclosed by the curved y=4x-x^2,and y=x^2-2x along the x-axis thanks so much help

*Thursday, January 19, 2017 by rajah*

**maths help calculus**

the area of a circle increasing at the rate of 3cm/sec.find the rate of change of the circumference when the radius is 2cm help plz

*Thursday, January 19, 2017 by rajah*

**Calculus**

Hello, I would like to make sure the answers to these questions are correct. 1. Using the shell method, what is the volume of a solid that is generated by rotating the region by y = x^2 and x = y^2 about the x axis. My Work: r = y h = sqrt(y) - y^2 2pi ∫[0,1] (y)((sqrt(y) - ...

*Wednesday, January 18, 2017 by Daisy*

**calculus**

how do you find the derivative of this (-x^2)/ (2) +2 and does it have any x intercepts, asypmtotes, or holes.

*Wednesday, January 18, 2017 by angie*

**Calculus**

How do you fine the derivative of (x-3)^-3

*Wednesday, January 18, 2017 by Angie*

**Pre-Calculus**

sketch f(x) such that f(x) is increasing on (-inf,-2) and f is decreasing on (-2,0), f(x) has point discontinuity at x=-2, f(x) has a horizontal asymptote of y=4, f(x) is an odd function.

*Wednesday, January 18, 2017 by Tod*

**Calculus Answer Check**

A particle moves along a line so that its position at any time t >= 0 is given by the function -t^3 + t^2 + 5t + 3, where p is measured in feet and t is measured in seconds. 1. Find the displacement during the first four seconds. My answer: 75 ft 2. Find the average ...

*Wednesday, January 18, 2017 by Anonymous*

**Calculus algebra review**

((1/2+h) -(1/2)) / h found LCD of numerator ((2)-(2+h)/2(2+h))/h is it 1

*Tuesday, January 17, 2017 by sarah*

**Calculus (Sequences)**

Hello, here is a picture of the question I am trying to solve, I believe the answer to be C, but I would just like some confirmation/correction. goo. gl/gWfhVn

*Tuesday, January 17, 2017 by Tim*

**AP Calculus**

Consider the function f(x) = 1/4x^4 - 5/3x^3 - 3/2x^2 + 15x - 3. A. Find the relative extrema for f(x); be sure to label each as a maximum or minimum. You do not need to find function values; just find the x-values. B. Determine the interval(s) where f(x) is increasing (if any...

*Monday, January 16, 2017 by Steph*

**Calculus**

I would like to make sure my answer is correct: Question: the base of a solid is the triangular region with the vertices (0,0), (2,0), and (0,4). Cross sections perpendicular to the x-axis are semicircles. Find the volume of this solid. My Work: ∫[0,2] (pi/2)(r^2)dx r = (-2x...

*Monday, January 16, 2017 by Rose*

**calculus**

Find the values for the following functions. If f(x)=2^x, show that f(x+3) -f (x-1)=15/2f(x) If G(x)= sin 2x, find G(0),G(1/4 pie),and G(7/8 pie)

*Monday, January 16, 2017 by jacob*

**calculus**

Find the domain of the variable x for which the following equations determine y as a real function of x. If G(x)= sin 2x, find G(0),G(1/4 pie),and G(7/8 pie) can someone help me please!

*Monday, January 16, 2017 by jacob*

**Vector Calculus**

Can someone help me with this please. A vector field in cylindrical polar co-ordinates is given by V = R Rˆ + R 3 s i n ( φ ) c o s ( φ ) φˆ + 3 z kˆ where Rˆ, φˆ, kˆ are the appropriate unit vectors. Translate this vector field into the Cartesian x, y, z co-ordinate...

*Monday, January 16, 2017 by Ariana*

**Calculus**

I would like to know if my answers are correct: Disclaimer: We are allowed to keep our answers in formula form 1. Use the washer method to find the volume of the solid that is generated by rotating the plane region bounded by y=x^2 and y = 2-x^2 about the axis y=-1 My Work: [...

*Monday, January 16, 2017 by Daisy*

**calculus**

Find the domain of the variable x for which the following equation determine y as a real function of x. y - xy = 5

*Sunday, January 15, 2017 by nabs*

**vector calculus**

Can someone help me with this please. A vector field in cylindrical polar co-ordinates is given by V = R Rˆ + R 3 s i n ( φ ) c o s ( φ ) φˆ + 3 z kˆ where Rˆ, φˆ, kˆ are the appropriate unit vectors. Translate this vector field into the Cartesian x, y, z co-ordinate...

*Sunday, January 15, 2017 by Ariana*

**Applied calculus**

A rectangular plot requires 2000 m of fencing to enclose it. If one of the dimensions is x meters, express the area y (m2) as a function of x. Determine the range of x.

*Saturday, January 14, 2017 by jayden*

**Calculus**

From each corner of a square of tin, 12 cm on a side, small squares of side x are removed and the edges are turned up to form an open box. Express the volume V (cm3) as a function of x. Determine the range of x.

*Saturday, January 14, 2017 by jayden*